Optimal Control for <i>k</i> × <i>k</i> Cooperative Fractional Systems

Abstract

This paper discusses the optimal control issue for elliptic k×k cooperative fractional systems. The fractional operators are proposed in the Laplace sense. Because of the nonlocality of the Laplace fractional operators, we reformulate the issue as an extended issue on a semi-infinite cylinder in Rk+1. The weak solution for these fractional systems is then proven to exist and be unique. Moreover, the existence and optimality conditions can be inferred as a consequence.

Keywords

• nonlocal operator
• fractional laplace operator
• weak solution
• optimality conditions
• cooperative systems